All the previous answers are right, as are you. You could make chocolate sauce with corn syrup, butter, I've even seen a hot water chocolate sauce, you could make a ganache with cream - all of these can be made to set smoothly but still be soft and sliceable. I've used this recipe before with good very nice results: https://food52.com/recipes/76662-alice-s-chocolate-butter-glaze. You can skip the marbling effect for a solid dark chocolate layer.
I used to have a client who ordered a cheesecake covered with dark chocolate ganache for every special occasion in their family. I once accused her of inventing events. She just smiled. It's very simple to make: equal quantities by weight of chopped dark chocolate (Guittard is a good one that you can dependably find in stores) and heavy cream heated just to the point of boiling, then poured over the chocolate. Let it sit for one minute, then stir slowly with a spatula. Don't use a whisk as is seen commonly on television; it creates bubbles that will mar the surface of the ganache once it is poured. Allow the ganache to cool at room temperature until the bowl is no longer warm to the touch, stirring it gently now and then with the spatula. At that point, pour it over the surface of your cheesecake. Smooth it ONCE with a metal spatula - more than once will streak it. Refrigerate overnight if possible. A hot, wet knife will cut beautifully through both the ganache and the cheesecake.
You could use corn syrup to keep the chocolate from setting, yes. What you describe is simply an ordinary chocolate syrup really. There are lots of recipes on the web to do that, some using corn syrup and some which don't, some using regular chocolate and others made with cocoa powder. You can look at a few of them to decide which sort will be best for the flavor profile and effect you are looking for.
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